江苏—西部能源需求—供给模型的余维2分岔  

CODIMENSION-TWO BIFURCATION OF JIANGSU-WESTERN ENERGY DEMAND-SUPPLY MODEL

作　　者：杨石柱[1] 杨新伟[1] 李君君[1] 

机构地区：[1]石家庄铁路职业技术学院交通系,石家庄050041

出　　处：《机械强度》2014年第2期171-178,共8页Journal of Mechanical Strength

基　　金：国家自然科学基金项目(11002093;11372196)资助~~

摘　　要：讨论江苏-西部能源系统的余维2动态分岔。借助中心流形定理对能源供给-需求系统进行降维,利用含有参数的可逆线性变换和近恒同非线性变换,得到系统的最简规范形。依据最简规范形与余维2普适开折等价,揭示了该系统的开折参数与原系统参数之间的关系,对能源内部优化、实现供给-消费的可持续发展提供了理论依据。给出该能源模型的数值仿真结果,得到时间历程图、二维相图和三维相图,验证了理论分析结果。Applying the center manifold theorem on dimensionality reduction, a reversible linear transformation and a nearidentity nonlinear transformation with parameters, the simplest normal form of the western energy demand-supply system is developed. Furthermore, its universal unfolding and the relationship between parameters of this system and the original system are obtained. The codimension-two bifurcation of the system is analyzed and the effect of each parameter on the whole system is revealed. Finally, using the numerical simulation with symbol algebra language Mathematica, 3-D phase diagram, 2-D phase diagram and time-history portraits are obtained, which verify the theoretical results.

关 键 词：能源系统 非线性系统 余维2分岔 最简规范形 

分 类 号：O322[理学—一般力学与力学基础]